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Finite element analysis of the panel flutter of stiffened shallow shells

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Abstract

The aeroelastic stability of flat plates and shallow cylindrical shells stiffened with stringers is investigated. In the case of a curved panel, the supersonic gas flow is parallel to its generatrix. A mathematical formulation of the dynamics problem is based on the variational principle of virtual displacements taking into account the work done by the inertial forces and aerodynamic pressure of the external supersonic gas flow determined according to the quasi-static aerodynamic theory. The solution is found by the finite element method in a three-dimensional formulation using the mode-superposition technique. The estimation of the shell stability is based on the analysis of complex eigenvalues of the system of equations calculated under gradually increasing aerodynamic pressure. The validity of the obtained results is confirmed by comparing them with the known solutions to a number of relevant problems. Numerical examples are used to analyze in detail the influence of the curvature ratio, the boundary conditions specified at the edges of the shallow shell, and the number of stringers on the boundary of stability loss. It is demonstrated that with an optimal arrangement of reinforcing elements, it is possible to achieve a significant increase in the critical parameters of the flutter.

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Acknowledgements

The paper was prepared in the framework of the program for the creation and development of the world-class scientific center “Supersonic” for 2020–2025 with the financial support of the Ministry of Education and Science of the Russian Federation (agreement no. 075-15-2022-329 of 21 April 2022).

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  1. Sergey A. Bochkarev, Sergey V. Lekomtsev and Valery P. Matveenko contributed equally to this work.

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  1. Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, 1, Acad. Korolev str., Perm, 614068, Russian Federation

    Sergey A. Bochkarev, Sergey V. Lekomtsev & Valery P. Matveenko

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Bochkarev, S.A., Lekomtsev, S.V. & Matveenko, V.P. Finite element analysis of the panel flutter of stiffened shallow shells. Continuum Mech. Thermodyn. 35, 1275–1290 (2023). https://doi.org/10.1007/s00161-022-01123-6

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